When One Form is Between Two Others: An Application of Biorthogonal Analysis

SYNOPSIS. This essay presents a method for measuring the degreeto which one biological outline form lies in between two others.The procedure does not measure forms separately, but rathercompares pairs of tensors expressing D'Arcy Thompson's "Cartesiantransformations" according to the biorthogonal formalism ofBookstein. In analogy with conventional methods, betweennessis computed as a similarity score, the cosine of a non- Euclideanangle between the tensors. The new quantities, size-betweennessand shapebetweenness, enable comparisons of form series againsta priori orderings intra- and interspecifically